## Speaking of Science Column April 26, 2009

### How fast am I going? It’s all relative, officer

As you sit comfortably in your chair reading this article, it may come as a surprise to learn that you are really traveling 816 miles per hour.

I know this may leave you incredulous because you don’t even feel your hair blowing.

The reason this statement can be made with a straight face is what scientists call the “frame of reference.” What’s the reference point when you make the statement?

When we think of the speed we are going, we implicitly think of the time it takes us to travel the distance from Point A (the reference point) to Point B. Scientists and engineers would write an equation to describe that as the “change in distance” divided by the “change in time.” If you traveled 92 miles in two hours, the equation would indicate that you averaged a speed of 46 mph.

But that is not the only speed you possess. Has it occurred to you that not only are you moving that 46 mph on highway, but that the highway also is on a spinning Earth? At Grand Junction, the speed of the rotating Earth is 816 mph toward the east. Now, relative to the Earth’s axis, you are traveling to the east at 816 mph plus or minus some portion of the 46 mph, depending on which direction your car was traveling relative to “east.”

Had your direction of movement on the highway been toward the west, your speed, relative to the Earth’s rotational axis, would be 770 mph to the east.

If we shift our “frame of reference” to the sun, the math gets trickier. The Earth is orbiting about the sun at a speed of 66,633 mph. With some appropriate mathematical manipulation, you could determine your speed in your car relative to the center of the sun. At the next level of complexity, the galaxy, you’d have to take into account the fact that the sun is also in motion about the center of our galaxy at a speed of approximately 500,000 mph.

Who would care about each of these situations? Let’s explore some of them. Your speed on the local highway is of vital interest to you, the driver, and to the officer near the corner with the radar gun.

Who cares about the rotational speed of a spot on the Earth’s surface? One individual is the person concerned with launching a spacecraft toward another planet. The rocket used must carry enough fuel to accelerate the spacecraft to a specific speed relative to the center of the Earth. By launching from Cape Kennedy, where the speed to the east is 911 mph, the energy of the Earth’s rotation saves you from having to carry the fuel to supply that equivalent energy. Some of the fuel saved can then be allocated to science instruments, which makes the mission more effective.

Persons interested in making sure the spacecraft arrives at the destination planet at exactly the correct time must take into account the speeds of the Earth and the destination planet around the sun. Those speeds are determined with Doppler tracking systems and some powerful computer capability.

Cosmologists, concerned with understanding the universe, including the motions and histories of stars (including our sun) and galaxies, are obliged to consider the speeds of stars around galaxies. Speeds of galaxies and stars in our expanding universe are important considerations as they continue to understand the history of the universe and to predict its future. Should we someday travel toward other stars, knowing these motions will be vitally critical to our success.

As you can see, changing the frame of reference changes numerical results. The article might have begun by alleging that you were reading this article while traveling over a half-million miles per hour, relative to the center of the galaxy.

What a concept!

Allan Conrad is a retired project manager for the Jet Propulsion Laboratory in Pasadena, Calif. He has volunteered for eight years at the Western Colorado Math & Science Center and is a math tutor at Grand Junction High School.

Is your head spinning with mathematical questions? E-mail .(JavaScript must be enabled to view this email address).

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